Optimization of time-dependent MORRAP for series–parallel system using improved NSGA-II in interval environment

This research proposes a novel time-dependent interval-valued function-based multi-objective reliability redundancy allocation problem (TIVF-MORRAP) focused on multi-stage series–parallel systems. Time is a critical factor in assessing system reliability and cost. The novel contribution of this study is the use of an interval-valued function (IVF) approach to manage uncertainties in component reliability, cost, and repair costs, with time as a key variable. The objective is to boost system reliability and minimize costs over time by efficiently allocating redundant components at each stage. The process ensures a restricted allocation of duplicates across all stages and the entire system. In this problem the reduction in component reliability and cost are modeled by the varying radius length along the inverse logarithmic spiral over time. Likewise, the escalation in component repair costs is depicted by the logarithmic spiral. In this study, NSGA-II-AGDV is introduced, a multi-objective evolutionary algorithm (MOEA) that combines NSGA-II (Non-dominated Sorting Genetic Algorithm-II) with agglomerative and divisive clustering algorithms and the Topsis method to solve the problem. Unlike NSGA-II, which utilizes crowding distance, many researchers have adopted a single clustering technique to improve diversity and limit the solution set size. The proposed algorithm integrates two clustering techniques, enhancing functionality while also reducing execution time. A benchmark problem verifies the proposed method, showing enhanced performance and better convergence to true Pareto optimal solutions compared to NSGA-II and NSGA-II with crowding distance elimination (NSGA-II-CDE) across various time values.